A tractable Walsh analysis of SAT and its implications for genetic algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Stochastic Local Search: Foundations & Applications
Stochastic Local Search: Foundations & Applications
Understanding elementary landscapes
Proceedings of the 10th annual conference on Genetic and evolutionary computation
When gravity fails: local search topology
Journal of Artificial Intelligence Research
Tuning local search for satisfiability testing
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Elementary bit string mutation landscapes
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Constant time steepest descent local search with lookahead for NK-landscapes and MAX-kSAT
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Quasi-elementary landscapes and superpositions of elementary landscapes
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
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Local search algorithms perform surprisingly well on the k -satisfiability (k -SAT) problem. However, few theoretical analyses of the k -SAT search space exist. In this paper we study the search space of the k -SAT problem and show that it can be analyzed by a decomposition. In particular, we prove that the objective function can be represented as a superposition of exactly k elementary landscapes. We show that this decomposition allows us to immediately compute the expectation of the objective function evaluated across neighboring points. We use this result to prove previously unknown bounds for local maxima and plateau width in the 3-SAT search space. We compute these bounds numerically for a number of instances and show that they are non-trivial across a large set of benchmarks.